Problem: Solve for $x$ and $y$ using elimination. ${-5x+y = -45}$ ${3x-y = 25}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-2x = -20$ $\dfrac{-2x}{{-2}} = \dfrac{-20}{{-2}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-5x+y = -45}\thinspace$ to find $y$ ${-5}{(10)}{ + y = -45}$ $-50+y = -45$ $-50{+50} + y = -45{+50}$ ${y = 5}$ You can also plug ${x = 10}$ into $\thinspace {3x-y = 25}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ - y = 25}$ ${y = 5}$